Journal
JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS
Volume 24, Issue 4, Pages 975-993Publisher
TAYLOR & FRANCIS INC
DOI: 10.1080/10618600.2014.948179
Keywords
Covariance estimation; High dimension; Invariance principles; Unsupervised learning
Categories
Funding
- NIH/NCI [R01 CA-149569, P01 CA-142538]
- NSF [DMS-1321692, DMS-1407241]
- FRG [DMS-1265202]
- NIH [1U54AI117924-01]
Ask authors/readers for more resources
Clustering methods have led to a number of important discoveries in bioinformatics and beyond. A major challenge in their use is determining which clusters represent important underlying structure, as opposed to spurious sampling artifacts. This challenge is especially serious, and very few methods are available, when the data are very high in dimension. Statistical significance of clustering (SigClust) is a recently developed cluster evaluation tool for high-dimensional low sample size (HDLSS) data. An important component of the SigClust approach is the very definition of a single cluster as a subset of data sampled from a multivariate Gaussian distribution. The implementation of SigClust requires the estimation of the eigenvalues of the covariance matrix for the null multivariate Gaussian distribution. We show that the original eigenvalue estimation can lead to a test that suffers from severe inflation of Type I error, in the important case where there are a few very large eigenvalues. This article addresses this critical challenge using a novel likelihood based soft thresholding approach to estimate these eigenvalues, which leads to a much improved SigClust. Major improvements in SigClust performance are shown by both mathematical analysis, based on the new notion of theoretical cluster index (TCI), and extensive simulation studies. Applications to some cancer genomic data further demonstrate the usefulness of these improvements.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available